Extensions of Locally Compact Abelian Groups. I
نویسندگان
چکیده
منابع مشابه
On component extensions locally compact abelian groups
Let $pounds$ be the category of locally compact abelian groups and $A,Cin pounds$. In this paper, we define component extensions of $A$ by $C$ and show that the set of all component extensions of $A$ by $C$ forms a subgroup of $Ext(C,A)$ whenever $A$ is a connected group. We establish conditions under which the component extensions split and determine LCA groups which are component projective. ...
متن کاملon component extensions locally compact abelian groups
let $pounds$ be the category of locally compact abelian groups and $a,cin pounds$. in this paper, we define component extensions of $a$ by $c$ and show that the set of all component extensions of $a$ by $c$ forms a subgroup of $ext(c,a)$ whenever $a$ is a connected group. we establish conditions under which the component extensions split and determine lca groups which are component projective. ...
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In this paper, we study the group Pext(C, A) for locally compact abelian (LCA) groups A and C. Sufficient conditions are established for Pext(C, A) to coincide with the first Ulm subgroup of Ext(C, A). Some structural information on pure injectives in the category of LCA groups is obtained. Letting C denote the class of LCA groups which can be written as the topological direct sum of a compactl...
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We define a new function-valued inner product on L2(G), called ?-bracket product, where G is a locally compact abelian group and ? is a topological isomorphism on G. We investigate the notion of ?-orthogonality, Bessel's Inequality and ?-orthonormal bases with respect to this inner product on L2(G).
متن کاملLocally compact abelian groups
These notes are a gloss on the first chapter of Walter Rudin’s Fourier Analysis on Groups, and may be helpful to someone reading Rudin. The results I do prove are proved in more detail than they are in Rudin. I caution that before reading the first chapter of that book it is know about the Gelfand transform on commutative Banach algebras because results from that are used without even stating t...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1971
ISSN: 0002-9947
DOI: 10.2307/1995449